IIB matrix model and regularized big bang

F R Klinkhamer

doi:10.1093/ptep/ptab059

Abstract

Abstract The large-N master field of the Lorentzian IIB matrix model can, in principle, give rise to a particular degenerate metric relevant to a regularized big bang. The length parameter of this degenerate metric is then calculated in terms of the IIB-matrix-model length scale.

Highlights

Einstein’s gravitational field equation [1] gives, in a cosmological context, the Friedmann–Lemaître– Robertson–Walker (FLRW) solution of a homogeneous and isotropic expanding universe with relativistic matter [2,3,4,5,6,7,8]
We have started an exploratory investigation of how a new physics phase can give an emerging classical spacetime with an effective metric where the big bang singularity has been tamed [9]
In order to be explicit, we have used the IIB matrix model [19,20], which has been suggested as a nonperturbative definition of type-IIB superstring theory

Summary

Introduction

Einstein’s gravitational field equation [1] gives, in a cosmological context, the Friedmann–Lemaître– Robertson–Walker (FLRW) solution of a homogeneous and isotropic expanding universe with relativistic matter [2,3,4,5,6,7,8]. The spacetime defect is, described by a degenerate metric with a vanishing determinant at t = 0 The details of this new cosmological solution are discussed in Refs. We pose the following question: does the master field of the Lorentzian IIB matrix model (assumed to be relevant for the physics of the Universe) give an emerging spacetime with a particular degenerate metric that corresponds to the regularized big bang solution of general relativity? We want to determine what would be required of the unknown functions ρav, h, and r (which trace back to the IIB-matrix-model master field), so that the integral (13a) gives the inverse metric (7), which has a divergent g00 component at t = 0

Basic idea

Core structure

First approximation

Conjectured final result

Conclusion